For general printer setup instructions see our:
Special Instructions for Configuring the HP Officejet e-All-in-One Printer (TPE-HPOFJE4630) under Ubuntu 12.04 LTS
General Instructions for adding printers & scanning functionality:
1. For scanning please add hplip-gui or HPLIP Toolbox found in the software center.
2. Open HPLIP Toolbox from your menu or search for it from your dash
3. Click the plus sign from the toolbar to add a new printer (or use the wizard if running HPLIP Toolbox for the first time, it'll prompt you if no printers are on the system)
Note: Some users (Debian 7 for instance) in step 2 need to run the HP utility as an administrative user if running it as a normal user does not work (the utility will ask you to restart CUPs, which will not solve the problem). To do this on Debian 7 and similar distributions open a terminal window and run: sudo hp-setup